An abstract framework for structured arguments is presented that instantiates Dung's (1995) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeat. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified.The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat, and extends it in several respects. Various rationality postulates are proven to be satisfied by the framework, and several existing approaches are proven to be a special case of the framework, including assumption-based argumentation and DefLog.

This paper builds on the recent ASPIC + formalism, to develop a general framework for argumentation with preferences. We motivate a revised definition of conflict free sets of arguments, adapt ASPIC + to accommodate a broader range of instantiating logics, and show that under some assumptions, the resulting framework satisfies key properties and rationality postulates. We then show that the generalised framework accommodates Tarskian logic instantiations extended with preferences, and then study instantiations of the framework by classical logic approaches to argumentation. We conclude by arguing that ASPIC + 's modelling of defeasible inference rules further testifies to the generality of the framework, and then examine and counter recent critiques of Dung's framework and its extensions to accommodate preferences.

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We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for each premise separately. Our approach allows the burden of proof for a premise to be assigned to a different party than the one who has the burden of proving the conclusion of the argument, and also to change the burden of proof or applicable proof standard as the dialogue progresses from stage to stage. Useful for modeling legal dialogues, the burden of production and burden of persuasion can be handled separately, with a different responsible party and applicable proof standard for each. Carneades enables critical questions of argumentation schemes to be modeled as additional premises, using premise types to capture the varying effect on the burden of proof of different kinds of questions.

This article gives a tutorial introduction to the ASPIC + framework for structured argumentation. The philosophical and conceptual underpinnings of ASPIC + are discussed, the main definitions are illustrated with examples and several ways are discussed to instantiate the framework and to reconstruct other approaches as special cases of the framework. The ASPIC + framework is based on two ideas: the first is that conflicts between arguments are often resolved with explicit preferences, and the second is that arguments are built with two kinds of inference rules: strict, or deductive rules, whose premises guarantee their conclusion, and defeasible rules, whose premises only create a presumption in favour of their conclusion. Accordingly, arguments can in ASPIC + be attacked in three ways: on their uncertain premises, or on their defeasible inferences, or on the conclusions of their defeasible inferences. ASPIC + is not a system but a framework for specifying systems. A main objective of the study of the ASPIC + framework is to identify conditions under which instantiations of the framework satisfy logical consistency and closure properties.

This article carries out a formal study of dialogue games for argumentation. A formal framework for such games is proposed which imposes an explicit reply structure on dialogues, where each dialogue move either attacks or surrenders to some earlier move of the other participant. The framework is flexible in several respects. It allows for different underlying logics, alternative sets of locutions and more or less strict rules for when they are allowed. In particular, it allows for varying degrees of coherence and flexibility when it comes to maintaining focus of a dialogue. Its formal nature supports the study of formal properties of specific dialogue protocols, especially on how they respect the underlying logic.

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